n4propsMeta: Empirical Power and Variance Reduction of an Updated Fixed...

Empirical Power and Variance Reduction of an Updated Fixed Effects Meta-Analysis with Binary Outcomes

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Description

This function provides the empirical power/variance reduction of an updated meta-analysis for
a vector of the number of clusters to randomize per group and a vector of estimates
of the ICC with a binary outcome measured using the (log) relative risk or odds ratio.

Usage

Arguments

data

A matrix with completed studies in each row. The first column contains the estimate
of the relative risk or odds ratio, the second column contains the 95 % lower limit and the third contains the 95 % upper limit.

k

A vector of the potential number of clusters to randomize to each of the treatment and control
groups. Note that this function assumes an equal allocation to treatment and control group status.

ICC

A vector of potential values of the ICC, these can be obtained from the cluster trials
themselves, or from the literature.

ICCDistn

The hypothetical distribution of the ICC values. This can be set to "fixed" (note that only one ICC value is accepted for this option), "unif" on the range [lower, upper], "normal", corresponding to the truncated
normal distribution (Turner et al, 2004), and "smooth" corresponding to the empirical smoothing option (Rotondi and Donner, 2009).

lower

The lower bound for the smoothing or unif options. Default value is zero.

upper

The upper bound for the smoothing or unif options. Default value is 0.25.

varRed

Logical; If varRed is set to TRUE, the proportionate reduction of variance is displayed
for the fixed effects meta-analysis.

m

The mean cluster size.

sdm

The standard deviation of the mean cluster size. This adds additional real-world variation
in the simulated study, using a normal model for large cluster sizes.

pC

The anticipated event in the control group. The anticipated treatment event is calculated
from the simulated effect size of the preliminary meta-analysis.

sdpC

The standard deviation of the control rate. This is to generate real-world variation
in the simulated study and can be precise or imprecise depending on the investigators preference.

iter

The number of iterations for each value of k and the ICC. This has a large impact
on computational time. Default is 1000.

alpha

The desired type I error rate for calculation of confidence limits for the
fixed effects level. For simplicity, this function assumes that each of the inputed lower
and upper limits that are 95 % confidence limits.

RR

Logical; Are the effect measures Relative Risks (TRUE) (default) or Odds Ratios (FALSE)? This is necessary
only for the calculation of variances.

Details

This function calculates the empirical power of an updated meta-analysis by a generalization
of Sutton et al. (2007) to the context of cluster randomized trials with
a binary outcome. The procedure is summarized in the accompanying manuscript. In short,
a hypothetical new study of a given size is simulated, then added to the meta-analysis. The
results are re-meta-analyzed and it is verified whether the pooled result is statistically significant,
or the appropriate reduction in variance of the pooled effect measure is recorded. Note
that the proportion of variance reduction and power may not always (strictly) decrease with k, as the simulation
exhibits individual-level variation.

Value

power

The power of the updated meta-analysis. Presented as a vector of
corresponding to the number of clusters.

varianceReduction

The proportionate reduction in variance for the number of clusters in the fixed effects meta-analysis.